Untitled Presentation

Multiple Choice

What is the meaning of the following symbol:

$$\int_a^bf\left(x\right)dx$$  

• The area from the curve to the x-axis from x = a to x = b

• The rate at which f(x) is changing from x = a to x = b

• The area from the curve to the y-axis from x = a to x = b

• The volume when the curve is rotated about the x-axis from x = a to x = b

Multiple Choice

Which of the following best describes the relationship between the derivative of an integral and evaluating definite integrals?

• They are unrelated concepts.

• The derivative of an integral gives the original function, while evaluating definite integrals gives the area under the curve.

• Both concepts only apply to polynomial functions.

• Evaluating definite integrals is the same as finding the derivative of an integral.

Multiple Choice

$$\int_0^1f\left(x\right)dx\$$  is

• Positive

• Negative

• 0

• Cannot be determined

Multiple Choice

Which of the following statements about definite integrals is correct based on the problems shown in slides 3 and 4?

• Definite integrals always require variable limits.

• Definite integrals can be evaluated using antiderivatives.

• Definite integrals cannot be solved with a calculator.

• Definite integrals are only used for area under curves.

Open Ended

Explain how a summation (sigma) expression can be converted into an equivalent definite integral. Provide an example to support your explanation.

Multiple Choice

If y = ∫ from 3 to x^2 of sin(t) dt, what is dy/dx?

• -cos(x^2)·2x

• sin(x^2)·2x

• -cos(x^2)

• sin(x^2)